Hello. I am studying second-order differential equations, and I am currently studying simple harmonic oscillations, like those in a spring-block system. When solving the differential equation, I get answers in the form of y^2=(adsbygoogle = window.adsbygoogle || []).push({});

[tex]x(t)^2=(c_1^2+c_2^2)(cos^2(\omega t)-(c_2^2/(c_1^2+c_2^2))sin^2(\pi/\omega))[/tex]

How can I convert this to the general form of the SHM equation:

[tex]x(t)^2=(c_1^2+c_2^2)cos^2(\omega t+\phi)[/tex]

where [tex]cos(\phi)=c_1/\sqrt{c_1^2+c_2^2}[/tex] and [tex]sin(\phi)=-c_2/\sqrt{c_1^2+c_2^2}[/tex]

I'm really close here, but I do not know how to use trig identities to convert the squared constant plus squared cosine function into just a single cosine function containing a shift. Thank you.

(PS- I am also trying to use Latex, so check back to see if I've edited the post to make it more readable. Hopefully, you can at least see what I'm going for)

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# Trig Identies

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